scholarly journals On Sharp Hölder Estimates of the Cauchy-Riemann Equation on Pseudoconvex Domains inCnwith One Degenerate Eigenvalue

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Sanghyun Cho ◽  
Young Hwan You
Keyword(s):  
Pseudoconvex Domain ◽  
Pseudoconvex Domains ◽  
Hölder Regularity ◽  
Holomorphic Curve ◽  
Riemann Equation ◽  
Degenerate Eigenvalue ◽  
Cauchy Riemann ◽  
Maximal Gain ◽  
Holder Regularity ◽  
Hölder Estimates

LetΩbe a smoothly bounded pseudoconvex domain inCnwith one degenerate eigenvalue and assume that there is a smooth holomorphic curveVwhose order of contact withbΩatz0∈bΩis larger than or equal toη. We show that the maximal gain in Hölder regularity for solutions of the∂¯-equation is at most1/η.

scholarly journals Stability of Hölder estimates for on pseudoconvex domains of finite type in ℂ2

1997 ◽  
Vol 148 ◽  
pp. 23-37
Author(s):  
S. Cho ◽  
H. Ahn ◽  
S. Kim
Keyword(s):  
Finite Type ◽  
Pseudoconvex Domain ◽  
Pseudoconvex Domains ◽  
The Stability ◽  
Hölder Estimates

AbstractLet Ω be a smoothly bounded pseudoconvex domain in ℂ2 and let bΩ be of finite type m. Then we prove the stability of Hölder estimates for under some perturbations of bΩ. As an application, we prove the Mergelyan property with respect to () norms for 0 ≤ α < 1/m.

The $\bar \partial $-problem on q-pseudoconvex domains with applications

2013 ◽  
Vol 63 (3) ◽  
Author(s):  
S. Saber
Keyword(s):  
Pseudoconvex Domain ◽  
Smooth Boundary ◽  
Pseudoconvex Domains ◽  
Lipschitz Boundary ◽  
Cauchy Riemann

AbstractFor a q-pseudoconvex domain Ω in ℂn, 1 ≤ q ≤ n, with Lipschitz boundary, we solve the $\bar \partial $-problem with exact support in Ω. Moreover, we solve the $\bar \partial $-problem with solutions smooth up to the boundary over Ω provided that it has smooth boundary. Applications are given to the solvability of the tangential Cauchy-Riemann equations on the boundary.

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